Questions tagged [strategy]

A puzzle whose solution is a methodological plan of action for realizing a specific goal.

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8
votes
6answers
1k views

Optimal next move in minesweeper game?

In order to solve this minesweeper game, what is the optimal next move? A description of the game can be found here: https://en.wikipedia.org/wiki/Minesweeper_(video_game) I do not have the answer ...
8
votes
1answer
514 views

Picking A Number Game

Alice and Bob play a game starting from Alice where Alice and Bob are supposed to write a number to the board, Then the game goes through several rounds between Alice and Bob with the rules below: ...
56
votes
22answers
16k views

Can you open the bathroom door? [closed]

This happened to me in a rental apartment and I had to be creative to solve it. The geniuses who designed the bathroom managed to fit a drawer about a centimeter behind the door, and eventually what ...
16
votes
2answers
1k views

Tic-Tac-Toe variant

To help people think this out, I've made a web game with increasingly difficult cpu players to allow brainstorming and testing strategies: cpu player, easiest (version 1 - at least 5-in-a-row is ...
9
votes
4answers
445 views

Number exchange game

Inigo and Vizzini are to have a battle of wits to the death. The rules are: Inigo is given two independent random numbers uniformly distributed between 0 and 1. Inigo chooses one of the numbers to ...
5
votes
3answers
2k views

Guessing a number game with a twist

Most of us have come across the problem in which a player chooses a number within a range $1-n$ and we have to guess that number by asking minimum no. of questions. That can be done by binary search(...
4
votes
2answers
2k views

When do missionaries and cannibals problems have solutions?

In the Missionaries and Cannibals problem: Three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, ...
1
vote
1answer
414 views

What is best strategy to multiple turn prisoners dilemma, when your opponents actions are hidden?

Best strategy for multiple turn prisoners dilemma is called tit for tat you start with cooperation and then repeat your opponents answer from previous turn. Is ...
15
votes
10answers
2k views

The barbarian king [duplicate]

A barbarian king wants his tribe to have more men than women, because men can fight and women cannot. to achieve this, he introduces the following law: Each couple has to produce babies until they ...
11
votes
3answers
830 views

16 Two Colored Line up v2

This is the follow-up question for 16 Two Colored Line Up This time, you are not supposed to solve it, but find the worst possible arrangement for each square, which will make the number of steps ...
19
votes
11answers
49k views

6 Tries to Guess a Number Between 1-100

After every time you guess, you're told if you're right, too high, or too low. Is there a strategy you can use to guarantee you'll get it on your 6th attempt (or lower)? I know a strategy to get it ...
9
votes
5answers
650 views

Salary sum with a twist

You've been considering your boss' offer, when you decide to try and sort things out for yourself. So, armed with your thought reading device, you set out to find the total salary of all the ...
1
vote
1answer
176 views

Another Unconventional Dice Blackjack game - is Nash equilibrium here?

This question is similar to This Dice Blackjack game - is there Nash equilibrium?, but the game rules are completely different. This Dice Blackjack is game for two. It is also played with fair six-...
0
votes
3answers
416 views

This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
4
votes
1answer
173 views

Turn based Number game

You and a friend take turns saying positive integers greater than one. You can't say a number that is a multiple of previous numbers or a sum of multiples of previous numbers. For example, if A says 3 ...
50
votes
3answers
6k views

Sliding Bolt Puzzle

You are in a room with two adjacent doors locked by four sliding bolts. The bolts are movable and block only one door at a time; however, you do not know which bolt currently is blocking which door. ...
7
votes
6answers
2k views

How will Y lose the game?

X and Y are playing a game. There are eleven coins on the table and each player must pick up at least one coin but not more than five in a turn. The person picking up the last coin loses. X starts. ...
20
votes
2answers
1k views

Titanicker Tic-Tac-Toe

This is something of a follow-on to Hugh Meyer's enjoyable "Titanic Tic-Tac-Toe." Fortunately, our intrepid heroes Xavier and Oliver have wrested away a bit of wreckage that some fellow named Jack was ...
2
votes
1answer
711 views

Move 2 or 3 spaces in this 5 by 5 grid

You have a 5 by 5 Board as shown. You start from the S (Center) position. You can: 1 Move TWO or THREE spaces only 2 You can move Vertically or Horizontally or Diagonally but only in a straight ...
9
votes
1answer
680 views

Pirate Puzzle Double Twist

Five pirates, fresh from their first bout of pillaging, return to their island base to celebrate and divide up the treasure. While this was their first time working together, the start of what they ...
0
votes
1answer
981 views

How could I have avoided this mistake in Minesweeper?

The puzzle grid pictured below is a prime example of the classic rush to judgment: I was so sure of my decision, but when I double-clicked to clear more cells, the cell to the left of the one I had ...
11
votes
1answer
10k views

How do I approach a “stuck” game of minesweeper?

I've played many a-game of minesweeper, and I frequently reach positions in which there is no logical, deterministic way to come to a conclusion about how I should solve the puzzle. How should I ...
6
votes
1answer
312 views

Maximize all weights

This question is related to What's the fewest weights you need to balance any weight from 1 to 40 pounds? You had 4 weights to balance any weight from $1$ to $40$ pounds which is answered previously ...
3
votes
2answers
325 views

Return to the Minotaur's Labyrinth

This is an extension of the puzzle The Minotaur's Labyrinth which is inspired by the comments from histocrat. You are trapped (again) in a chamber at the center of the minotaur's labyrinth. There are ...
5
votes
1answer
512 views

What will be the last Sudoku number to be filled?

When I am completing a Sudoku puzzle, there are always two last numbers to fill. Maybe it is just my puzzle solving approach or maybe it is inherent to Sudoku. I got wondering, would everyone who ...
14
votes
3answers
2k views

Rubik's cube two-person game

I will define the game as follows: There are two players, the "Solver" and the "Unsolver". The Solver's goal is to return the cube to it's standard solved state. Likewise, the Unsolver's goal is to ...
14
votes
2answers
2k views

Tic-Tac-Toe Without a Predefined Board

On a warm and uneventful summer day, John and Mary passed the time by playing games of Tic-Tac-Toe, taking sticks and drawing in the soil. John and Mary are both child prodigies, so within two rounds ...
6
votes
3answers
3k views

Impossible 100 Balls Game

You are trying to make an impossible game where there are $100$ balls numbered from $1$ to $100$ and ordered in the worst case and put next to each other. The player is supposed to order the balls ...
21
votes
4answers
6k views

Picking up stones

Here is puzzle that was lifted from an old essay of mine, that was adapted from a puzzle in an old puzzle book. The great shah has invited a young boy into his palace as a student. While he is not ...
8
votes
2answers
495 views

Guess n binary digits

There's a N (1 ≤ N ≤ 1 000; N is pair) digit binary number and you have a maximum of 2050 guesses to find out which is it. With each try, you will know one of the following: You got it right (100%); ...
27
votes
9answers
2k views

Winnie-the-Pooh and the 27 honey pots

Winnie-the-Pooh keeps his $27$ honey pots in the larder. Each pot contains up to $1$ kilogram of honey, and different pots contain different quantities of honey. All $27$ pots together contain $17$ ...
14
votes
1answer
479 views

Rook Game on a Chessboard - Take 2

This question is inspired by this puzzle. You have an $m \times n$ chessboard with $m \le n$. Alice and Bob alternately move the rook (horizontally or vertically, through any number of squares). As ...
2
votes
1answer
403 views

Numberlink strategy

Note: This is not asking for a general strategy, you can find that here. Is the following a valid strategy in solving Numberlink (Flow Free) puzzles (I like to call it 'unwrapping the grid'): ...
26
votes
5answers
5k views

You trolls, get out of my party!

You have invited $2017$ of your acquaintances to a party. But after they all arrive, you come to know from a reliable source that each of your guests is either a troll or a true friend. You don't know ...
7
votes
3answers
810 views

Dinosaur Egg Drop v2

This question is a little different and kinda follow-up version of Dinosaur Egg Drop 1- You have 100 story building and 6 Apatosaurus dinosaur eggs. 2- You have 81 story building and 3 ...
29
votes
7answers
114k views

Clever ways to solve Mastermind?

Is there any specific way to solve Mastermind? Apart from the first step that is pure chance, is there any way to continue based on the colors that you think are correct?
11
votes
1answer
636 views

A Tic-Tac-Toe variant with three marks - winning strategy and chances

We start with a usual $3 \times 3$ grid, $3$ different marks (say, $X, O, I$) and $2$ players. Player $A$ has to make a vertical, horizontal or diagonal line made of $3$ identical marks (XXX, OOO or ...
5
votes
1answer
281 views

Find k defective balls out of n balls

There are $n$ balls out of which $k$ are defective, where $k<n/2$. All defective balls have the same weight $w$, and all non-defective balls have the same weight $v$ with $v<w$. Determine all ...
34
votes
1answer
6k views

Coins on a table

John and Jane are playing a game. They both go to the bank and get 1000 euros in 2 euros. So each of them has 500 euros at stake. They then find a large rectangle table and decide who wins the ...
3
votes
3answers
586 views

A variation of the poisoned bottle problem

Old story. The King has received X=950 bottles of wine, exactly one of which is poisoned enough to kill a man exactly 24 hours after ingestion. The King wants to feed some N prisoners some mix of the ...
5
votes
2answers
589 views

Lead the murderers out

Imagine you are in a big hall. Except you, there are 20 other people. In the beginning, you have different pieces of paper: ...
28
votes
3answers
2k views

Finding digits that sum to 15

Rand and Rubio are playing a game in which they each take turns to pick a digit between 1 and 9, without replacement (i.e. all digits chosen are distinct). If one of them manages to get three digits ...
2
votes
5answers
496 views

Coin Splitting Game [closed]

There are 8 coins to be divided between A and B. A first makes an offer of how to divide the 8 coins between them. If B refuses A’s offer, then now it is B’s turn to make the offer, but this time 4 ...
11
votes
6answers
10k views

1 Fake Coin among N Amount of coins

You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale. You are asked to find the fake coin in totally 5 times weighing on the Pan ...
7
votes
1answer
846 views

Tic Tac Toe Recursive

Related: Connect 4 Recursive We have a mega tic tac toe grid. Each of the nine cells of the mega grid has a smaller tic tac toe grid. In total we have 81 cells that can be filled. (Maybe imagine a ...
7
votes
1answer
561 views

Connect 4 Recursive

Here is a variant of the standard connect 4. There are seven connect 4 grids (size 6 by 7) numbered 1 to 7. Each grid has the columns numbered 1 to 7. The person who starts selects any one of the ...
39
votes
1answer
2k views

Polynomial game with Devil

You die, and awake in Hell. Satan awaits you, and has prepared a curious game. On a blackboard, he has written the polynomial $x^2+x+666$. He explains the rule: On each day at $12$ noon, you must ...
7
votes
3answers
2k views

Is it always safe to click first in the lower lefthand corner of a Minesweeper puzzle?

I always start a Minesweeper puzzle in Windows by clicking the cell in the lower left corner. Even though I have never seen a bomb there, how sound is this strategy? Is it possible that some time in ...
6
votes
2answers
561 views

Hopping Frogs puzzle variant

There is an old puzzle which has various names such as Toads and Frogs, Jumping Frogs, Hopping Frogs, Leap Frog, etc., and which has been asked here before. I'd like to share a variant of this puzzle ...
5
votes
2answers
5k views

Is there an algorithm for the Rubik's 360?

Is there an algorithm to help me solve the Rubik's 360? Usually I just do it at random, but I rarely succeed.